Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.     

Lipid dependence of the channel properties of a colicin E1-lipid toroidal pore

Colicin E1 belongs to a group of bacteriocins whose cytotoxicity toward Escherichia coli is exerted through formation of ion channels that depolarize the cytoplasmic membrane. The lipid dependence of colicin single-channel conductance demonstrated intimate involvement of lipid in the structure of this channel. The colicin formed "small" conductance 60-picosiemens (pS) channels, with properties similar to those previously characterized, in 1,2-dieicosenoyl-sn-glycero-3-phosphocholine (C20) or thinner membranes, whereas it formed a novel "large" conductance 600-pS state in thicker 1,2-dierucoyl-sn-glycero-3-phosphocholine (C22) bilayers. Both channel states were anion-selective and voltage-gated and displayed a requirement for acidic pH. Lipids having negative spontaneous curvature inhibited the formation of both channels but increased the ratio of open 600 pS to 60 pS conductance states. Different diameters of small and large channels, 12 and 16 A, were determined from the dependence of single-channel conductance on the size of nonelectrolyte solute probes. Colicin-induced lipid "flip-flop" and the decrease in anion selectivity of the channel in the presence of negatively charged lipids implied a significant contribution of lipid to the structure of the channel, most readily described as toroidal organization of lipid and protein to form the channel pore.     

Temperature dependence of the rotation and hydrolysis activities of F1-ATPase

F₁-ATPase, a water-soluble portion of the enzyme ATP synthase, is a rotary molecular motor driven by ATP hydrolysis. To learn how the kinetics of rotation are regulated, we have investigated the rotational characteristics of a thermophilic F₁-ATPase over the temperature range 4-50°C by attaching a polystyrene bead (or bead duplex) to the rotor subunit and observing its rotation under a microscope. The apparent rate of ATP binding estimated at low ATP concentrations increased from 1.2 × 10⁶ M⁻¹ s⁻¹ at 4°C to 4.3 × 10⁷ M⁻¹ s⁻¹ at 40°C, whereas the torque estimated at 2 mM ATP remained around 40 pN·nm over 4-50°C. The rotation was stepwise at 4°C, even at the saturating ATP concentration of 2 mM, indicating the presence of a hitherto unresolved rate-limiting reaction that occurs at ATP-waiting angles. We also measured the ATP hydrolysis activity in bulk solution at 4-65°C. F₁-ATPase tends to be inactivated by binding ADP tightly. Both the inactivation and reactivation rates were found to rise sharply with temperature, and above 30°C, equilibrium between the active and inactive forms was reached within 2 s, the majority being inactive. Rapid inactivation at high temperatures is consistent with the physiological role of this enzyme, ATP synthesis, in the thermophile.     

Modeling the stability of the human glenohumeral joint during external rotation

An analytical model of the human glenohumeral joint was developed to predict glenohumeral kinematics and investigate how the glenohumeral capsule and articular contact between the humeral head and the glenoid stabilize the joint. This was performed during a simulation of an apprehension clinical exam or the cocked phase of throwing, when the humerus is susceptible to anterior instability or dislocation. Contact between the joint surfaces was modeled using a deformable articular contact method and the capsule was modeled as five elements with the ability to wrap around the surface of the humeral head. Experimental measurements (Novotny et al., Journal of Shoulder and Elbow surgery, 1998, 7, 629-639) provided geometric data from four in vitro specimens and kinematic results to validate model predictions. Material properties were taken from the literature. An equilibrium approach was used with the forces and moments produced by the ligaments and surface contact balanced against those applied externally to the humerus during external rotation of the abducted and extended humerus. The six equilibrium equations were solved for the position and orientation of the humerus. The center of the humeral head translated posteriorly and superiorly with external rotation. Model predictions for translational and rotational ranges of motion were not significantly different from experimental findings; however, at individual moment increments, the model underestimated the external rotation and overestimated the superior-inferior position of the humerus relative to the glenoid. The anterior band of the inferior glenohumeral ligament increased in tension with external rotation, while the axillary pouch and posterior band decreased in tension. Contact area, stress and force increased with external rotation and the contact area moved posteriorly and inferiorly around the rim of the glenoid. The model results provide information on how the relationship between the ligament element tensions and contact forces may act to avoid glenohumeral instability.     

Effect of density variations along ion drift trajectories on the poloidal and toroidal rotation velocities of a collisionless tokamak plasma

The effect of plasma density variations along ion drift trajectories on the ion velocity distribution function at a given point on a tokamak magnetic surface is studied. The observed distortion of the distribution function can be interpreted as a poloidal (or toroidal) plasma rotation that is additional to the neoclassical rotation. Due to this additional rotation, the velocity of the toroidal plasma rotation is different on the low-and high-field sides of the same magnetic surface. In the case of large ion density gradients, the poloidal rotation velocity on the same magnetic surface can have different signs at different poloidal angles.     

Parameter dependence of correlation between the Shannon index and members of parametric diversity index family

We present detailed data on correlation of the Shannon diversity index with members of Hill's and Hurlbert's parametric index family. The correlation reaches its maximum in both cases at a definite parameter value. These specified data on correlation are exploitable when applying the above diversity indices. Namely, in case of their parallel use with the Shannon index a strong correlation between the indices should be avoided. The investigations were carried out on sets of moth and fly collections.Moreover, we hypothesized that a smaller distance between so-called sensitivity profiles of diversity indices predicts a larger correlation between the indices concerned. Based on investigations of the sensitivity profile distance between the Shannon index and members of parametric diversity index family as a function of index parameter, we point out that on the whole the above hypothesis is true. This makes possible to estimate the correlation of two diversity indices omitting troublesome index calculations on a large set of abundance lists.     

Cutting edge: precursor frequency affects the helper dependence of cytotoxic T cells.

Generation of CTL immunity often depends on the availability of CD4 T cell help. In this report, we show that CTL responses induced by cross-priming can be converted from CD4-dependent to CD4-independent by increasing the frequency of CTL precursors. In the absence of CD4 T cells, high numbers of CTL precursors were able to expand in number and become effector CTL. The ability of high frequencies of CD8 T cells to override help was not due to their ability to signal CD40 via expression of CD154. These findings suggest that when precursor frequencies are high, priming of CD8 T cell responses may not require CD4 T cell help.     

Modeling the length dependence of isometric force in human quadriceps muscles

Functional electrical stimulation is used to restore movement and function of paralyzed muscles by activating skeletal muscle artificially. An accurate and predictive mathematical model can facilitate the design of stimulation patterns that produce the desired force. The present study is a first step in developing a mathematical model for non-isometric muscle contractions. The goals of this study were to: (1) identify how our isometric force model's parameters vary with changes in knee joint angle, (2) identify the best knee flexion angle to parameterize this model, and (3) validate the model by comparing experimental data to predictions in response to a wide range of stimulation frequencies and muscle lengths. Results showed that by parabolically varying one of the free parameters with knee joint angle and fixing the other parameters at the values identified at 40 degrees of knee flexion, the model could predict the force responses to a wide range of stimulation frequencies and patterns at different muscle lengths. This work showed that the current isometric force model is capable of predicting the changes in skeletal muscle force at different muscle lengths.     

Modeling mitral valve stenosis: A parametric study on the stenosis severity level

New computational techniques providing more accurate representation of human heart pathologies could help uncovering relevant physical phenomena and improve the outcome of medical therapies. In this framework, the present work describes an efficient computational model for the evaluation of the ventricular flow alteration in presence of mitral valve stenosis. The model is based on the direct numerical simulation of the Navier–Stokes equations two-way coupled with a structural solver for the left ventricle and mitral valve dynamics. The presence of mitral valve stenosis is mimicked by a single-parameter constraint acting on the kinematics of the mitral leaflets.Four different degrees of mitral valve stenosis are considered focusing on the hemodynamic alterations occurring in pathologic conditions. The mitral jet, generated during diastole, is seen to shrink and strengthen when the stenosis gets more severe. As a consequence, the kinetic energy of the flow, the tissues shear stresses, the transvalvular pressure drop and mitral regurgitation increase. It results that, as the stenosis severity level increases, the geometric and effective orifice areas decrease up to 50% with respect the normal case due to the reduced leaflets mobility and stronger blood acceleration during the diastolic phase. The modified intraventricular hemodynamics is also related to a stronger pressure gradient that, for severe stenosis, can be more than ten times larger than the healthy valve case. These computational results are fully consistent with the available clinical literature and open the way to the virtual assessment of surgical procedures and to the evaluation of prosthetic devices.     

Modeling of a foamed emulsion bioreactor: II. model parametric sensitivity

The sensitivity of a conceptual model of a foam emulsion bioreactor (FEBR) used for the control of toluene vapors in air was examined. Model parametric sensitivity studies showed which parameters affect the removal of toluene (as model pollutant) in the FEBR the most significantly, and enabled definition of the limits of the process. Detailed examination of the results indicated that the process is highly complex and that both mass transfer and kinetic limitations can coexist in the bioreactor system. These results will help with the optimization of the design and operation of FEBRs.     

Cutting edge: monovalency of CD28 maintains the antigen dependence of T cell costimulatory responses

CD28 and CTLA-4 are the major costimulatory receptors on naive T cells. But it is not clear why CD28 is monovalent whereas CTLA-4 is bivalent for their shared ligands CD80/86. We generated bivalent CD28 constructs by fusing the extracellular domains of CTLA-4 or CD80 with the intracellular domains of CD28. Bivalent or monovalent CD28 constructs were ligated with recombinant ligands with or without TCR coligation. Monovalent CD28 ligation did not induce responses unless the TCR was coligated. By contrast, bivalent CD28 ligation induced responses in the absence of TCR engagement. To extend these findings to primary cells, we used novel superagonistic and conventional CD28 Abs. Superagonistic Ab D665, but not conventional Ab E18, predominantly ligates CD28 bivalently at low CD28/Ab ratios and induces Ag-independent T cell proliferation. Monovalency of CD28 for its natural ligands is thus essential to provide costimulation without inducing responses in the absence of TCR engagement.     

Modeling the dependence between the number of trials and the success probability in binary trials

A model for binary trials based on a bivariate generalization of the Poisson process for both the number of successes and number of trials with the transition rates dependent on the accumulating numbers of successes and trials is used to reanalyze some recently published data of Zhu, Eickhoff, and Kaiser (2003, Biometrics59, 955-961). This modeling admits alternative distributions for the numbers of trials and the numbers of successes conditional on the number of trials which generalize the Poisson and binomial distributions, without some of the restrictions apparent in the beta-binomial-Poisson mixed modeling of Zhu et al. (2003). Some quite marked differences between the results of this analysis and those described in Zhu et al. (2003) are apparent.     

Modeling the dependence of the period of intracellular Ca2+ waves on SERCA expression

Contrary to intuitive expectations, overexpression of sarco-endoplasmic reticulum (ER) Ca(2+) ATPases (SERCAs) in Xenopus oocytes leads to a decrease in the period and an increase in the amplitude of intracellular Ca(2+) waves. Here we examine these experimental findings by modeling Ca(2+) release using a modified Othmer-Tang-model. An increase in the period and a reduction in the amplitude of Ca(2+) wave activity are obtained when increases in SERCA density are simulated while keeping all other parameters of the model constant. However, Ca(2+) wave period can be reduced and the wave amplitude and velocity can be significantly increased when an increase in the luminal ER Ca(2+) concentration due to SERCA overexpression is incorporated into the model. Increased luminal Ca(2+) occurs because increased SERCA activity lowers cytosolic Ca(2+), which is partially replenished by Ca(2+) influx across the plasma membrane. These simulations are supported by experimental data demonstrating higher luminal Ca(2+) levels, decreased periods, increased amplitude, and increased velocity of Ca(2+) waves in response to increased SERCA density.     

Modeling the onset of drug dependence: a consideration of the requirement for protein synthesis

It has been proposed, with some supporting evidence, that development of opiate tolerance and dependence requires protein synthesis. However, a quantitative, biologically based model within which to analyse and support the data has been lacking. Utilizing such a framework or model, we recently compared the time course of onset of opiate dependence in laboratory animals, with the mathematical time course of general changes in protein levels. Not only did the time course of onset of dependence parallel the time course of increasing levels of a protein, but also the half-life of the putative protein required by the model was very similar to those of many brain proteins. In this study, we have more extensively tested the model by producing and examining a much more detailed and surprisingly complex time course of the onset of dependence. Applying the protein synthesis time course model to the data suggested the presence of two distinct components of dependence, an early transient component and a later long-lasting component. These components appear to correspond to acute and chronic dependence, respectively. The protein synthesis hypothesis more readily applies to the chronic dependence portion. Because consideration of the model can generate components that correspond to accepted and well-known components of dependence, both the utility of the model as well as the hypothesis that opiate dependence at least partially requires protein synthesis are supported. It is also possible that individual components of the withdrawal syndrome have individual and unique rate limiting mechanisms. In any case, time course analysis may be helpful in revealing underlying mechanisms of change.     

Cutting edge: the dependence of plasma cells and independence of memory B cells on BAFF and APRIL

Memory B (B(MEM)) cells and long-lived bone marrow plasma cells (BM-PCs) persist within local environmental survival niches that afford cellular longevity. However, the factors supporting B(MEM) cell survival within the secondary lymphoid organs and allowing BM-PC persistence in the bone marrow remain poorly characterized. We report herein that long-lived B(MEM) cell survival and function are completely independent of BAFF (B cell-activating factor of the TNF family) or APRIL (a proliferation-inducing ligand). Thus, B(MEM) cells represent the only mature B2 lineage subset whose survival is independent of these ligands. We have previously shown that the TNFR family member receptor BCMA (B cell maturation Ag) is a critical survival receptor for BM-PC survival in vivo. We identify in this study the ligands critical for BM-PC survival and show that either BAFF or APRIL supports the survival of BM-PCs in vivo. These data define the BAFF/APRIL-dependent and -independent components of long-lived humoral immunity.     

Modeling the dependence between number of trials and success probability in beta-binomial-Poisson mixture distributions

Beta-binomial models are widely used for overdispersed binomial data, with the binomial success probability modeled as following a beta distribution. The number of binary trials in each binomial is assumed to be nonrandom and unrelated to the success probability. In many behavioral studies, however, binomial observations demonstrate more complex structures. In this article, a general beta-binomial-Poisson mixture model is developed, to allow for a relation between the number of trials and the success probability for overdispersed binomial data. An EM algorithm is implemented to compute both the maximum likelihood estimates of the model parameters and the corresponding standard errors. For illustration, the methodology is applied to study the feeding behavior of green-backed herons in two southeastern Missouri streams.     

The precipitation of toroidal collagen fibrils

The morphology of aggregates of calf-skin tropocollagen, precipitated by continuous injection into neutral phosphate buffers at 35 degrees , has been studied by electron microscopy. Although most of the collagen is precipitated as normal native fibrils, a small proportion forms closed toroidal structures having the usual native band-interband pattern. Theoretical considerations, based on elastic energies in a general microfibril model, predict that the toroids should have a simple super-helical structure, and this is not inconsistent with the observations. From the theoretical energies it was possible to estimate a crude lower limit of 3kcal./mole for the free energy of association of the tropocollagen macromolecules.